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# Michaelis-menten kinetics

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### Michaelis-menten kinetics

1. 1. Seminar on MICHAELIS MENTEN KINETICS PRESENTED BY MOHAMMED MUNAWAR ALI (M.PHARM. 1 ST SEMESTER) DEPT. OF PHARMACEUTICS ST. PETER’S INSTITUTE OF PHARMACEUTICAL SCIENCES,VIDYANAGAR, HANAMKONDA. 506001.AFFILIATED TO KAKATIYA UNIVERSITY
2. 2. C ONTENTS Introduction Some pharmacokinetic aspects of Michaelis-Menten equation. In vivo estimation of Km and Vm Estimation of pharmacokinetic parameters concerned Other Non-linear Processes Problems in quantifying non-linear kinetics Conclusion References 2
3. 3. I NTRODUCTION Linear kinetics, wherein the change in plasma concentration of drug due to absorption, distribution, binding, metabolism or excretion is proportional to its dose whether administered as single or multiple doses. Drug biotransformation, renal tubular secretion, and biliary secretion usually require enzyme or carrier systems. These systems are relatively specific with respect to substrate and have finite capacities, such processes are called capacity limited process; commonly called non-linear pharmacokinetics. 3
4. 4.  The pharmacokinetics of such drugs which follow non- linear are said to be dose dependent, mixed order or capacity limited process. The kinetics of capacity limited process are best explained by Michaelis-Menten equation, given as This equation is derived from the following scheme.  E = conc. of enzyme K-1 K  C = conc. of drugE+C K1 EC 2 E+M  EC= conc. of enzyme-drug complex  M = conc. of metabolite  K2 and K-1 = first order rate constants  K1 = second order rate constant 4
5. 5. Table-1Causes of non linearity Examples AbsorptionSaturable transport in gut wall RiboflavinDrug comparatively insoluble GriseofulvinSaturablegut wall or hepatic metabolism on first pass Salicylamide, propranololPharmacologic effect on GI motility Metoclopramide, chloroquineSaturable gastric or GI decomposition Some penicillins DistributionSaturable plasma protein binding Phenylbutazone, salicylatesSaturable tissue binding NaproxenSaturable transport into or out of tissues methotrexate Renal eliminationActive secretion Penicillin GActive reabsorption Ascorbic acidChange in urine pH Salicylic acidSaturable plasma protein binding Salicylic acidNephrotoxic effect at higher doses Amino glycosidesDiuretic effect Theophylline, alcohol Extra renal eliminationCapacity limited metabolism Phenytoin, theophyllineEnzyme saturation or co-factor limitation Salicylic acid, alcoholSaturable biliary secretion Tetracycline, indomethacinEnzyme induction CarbamazepineHepatotoxic at higher doses AcetaminophenSaturable plasmaproteinbinding Phenylbutazone 5Altered hepatic blood flow PropranololMetabolite inhibition. Diazepam
6. 6. SOME PHARMACOKINETICASPECTS Three conditions are considered here where the michaelis-menten equation alter depending. i) when Km=C -dC/dt= Vm/2 ii) when Km>>> C -dC/dt= (Vm/Km)C iii) when Km<<< C -dC/dt= Vm Fig 1 6 Source: Milo Gibaldi, Pharmacokinetics
7. 7. In vivo ESTIMATION OF K m AND V m When drug is administered via IV injection, eliminated by single capacity limited process. Solving the equation we get, Modified form of which is, Conversion to common logarithmic form and solving for log C, Fig 2. Source: Milo Gibaldi, Pharamacokinetics 7
8. 8.  Lineweaver-Burk equation Hanes-woolf plot Woolf-Augustinsson-Hofstee equation Direct method 8 Fig 3. Source: Milo Gibaldi, Pharamacokinetics
9. 9.  Considering the drug elimination involving one capacity limited process and one or more first order processes, the rate of elimination is represented as, Km<<<C Km>>>C Plot -d ln C/dt Vs 1/C where slope is Vm. To get Km the eq. is considered at lower concentration. 9
10. 10. Fig 3. Fig 4.Source: Milo Gibaldi, Pharamacokinetics Source: Milo Gibaldi, Pharamacokinetics 10
11. 11. USAGE OF URINE DATA K’ V’m kmu K’m V’m is maximum rate of metabolite,K’ & kmu are first order rate constants,K’m is michaelis-menten’s constant,Cm is plasma drug conc. at midpoint ofcollection interval. Fig 5. 11 Source: Milo Gibaldi, Pharamacokinetics
12. 12. ESTIMATION OFPHARMACOKINETIC PARAMETERSCONCERNED Clearance(ClS), Half-life (t1/2) and Volume of distribution. In linear kinetics, While in non-linear kinetics, or 12
13. 13.  For the case where linear pathways of elimination in parallel with a non-linear process, 13
14. 14. OTHER NON-LINEAR PROCESSESI. CHRONOPHARMACOKINETICS It refers to temporal changes in rate processes like absorption and elimination which may be either cyclical or noncyclical. aminoglycosideII. ENZYME INDUCTION Repeated doses of Carbamazepine induces the enzymes responsible for its elimination. 14
15. 15. III. PROTEIN BINDING Plasma level- time profiles of two drugs A and B where A is 90% protein bound and B does not bind with plasma protein.Ex: Valproic acid. Fig 6. Source: Leon Shargel, Applied biopharmaceutics Pharamacokinetics 15
16. 16. PROBLEMS IN QUANTIFYING NON-LINEARPHARMACOKINETICS Estimation of Km and Vm assuming multi compartment would be more approporiate rather than considering a one compartment model. One more problem encounters when a drug is eliminated via more than one capacity limited processes.[Sedmen et al.] No problem in Km, when it is in factor of 3. Drugs which effect the hepatic blood flow in turn effecting the rate of elimination. The mechanism by which these act are altering the cardiac outflow. 16
17. 17. CONCLUSION Non linear pharmacokinetics is dose dependent and does not occur significantly at lower doses of drug. Probable reasons to occur may be attributed to change in physiologic system or saturation or protein binding or enzyme induction. Though the level of complexity increases when it is applied more realistic, assuming the process in a single compartment several pharmacokinetic parameters are estimated concerned. 17
18. 18. REFERENCES G. Levy. Pharmacokinetics of salicylate elimination in man. J. Pharm. Sci. 54:959 (1965). K. Arnold and N. Gerber. The rate of decline of diphenylhydantoin in human plasma. Clin. Pharmacol. Ther. 11: 121 (1970). N. Gerber and J. G. Wagner. Explanation of dose-dependent decline of diphenylhydantoin plasma levels by fitting to the integrated form of Michaelis-Menten equation. Res. Commun. Chem. Pathol. Pharmacol. 3: 455 (1972). L. Martis and R. H. Levy. Bioavailability calculations for drugs showing simultaneous first -order and capacity-limited elimination kinetics. J. Pharmacokinet. Biopharm. 1: 283 18 (1973) .
19. 19.  T. Tsuchiya and G. Levy. Relationship between dose and plateau levels of drugs eliminated by parallel first-order and capacity- limited kinetics. J. Pharm. Sci. 61:541(1972). W. H. Pitlick and R. H. Levy. Time-dependent kinetics: I. Exponential autoinduction of carbamazepine in monkeys. J. Pharm. Sci. 66:647 (1977).BIBILIOGRAPHY Milo Gibaldi and Donald Perrier. Pharmacokinetics. Second edition. Volume 15. Marcel Dekker INC. 272-289 (2006). Leon Shargel, Susanna Wu-Pong and Andrew B.C Yu. Non-linear Pharmacokinetics. Applied Biopharmaceutics and Pharmacokinetics. Fifth edition. The McGraw-Hill Companies, INC. 240-242 (2007) 19
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